Quantum Gravity: Can It Be Empirically Tested?

Claus Kiefer (left) and Manuel Krämer (right) 

[Every year (since 1949) the Gravity Research Foundation honors best submitted essays in the field of Gravity. This year's prize goes to Claus Kiefer and Manuel Krämer for their essay "Can Effects of Quantum Gravity Be Observed in the Cosmic Microwave Background?". The five award-winning essays will be published in a special issue of the International Journal of Modern Physics D (IJMPD). Today we present here an article by Claus Kiefer and Manuel Krämer on their current work. -- 2Physics.com ]

Authors: Claus Kiefer and Manuel Krämer

Affiliation: University of Cologne, Germany 

Quantum theory seems to be a universal framework for physical interactions. The Standard Model of particle physics, for example, is described by a quantum field theory of the strong and electroweak interactions. The only exception so far is gravity, which is successfully described by a classical theory: Einstein's theory of general relativity. The general expectation, however, is that general relativity is incomplete and must merge with quantum theory to a fundamental theory of quantum gravity [1,2]. One reason is the singularity theorems in Einstein's theory, the other is the universal coupling of gravity to all forms of energy and thus to the energy of all quantum fields.

2Physics articles by past winners of the Gravity Research Foundation award:
Mark Van Raamsdonk (2010): "Quantum Gravity and Entanglement"
Alexander Burinskii (2009): "Beam Pulses Perforate Black Hole Horizon"
T. Padmanabhan (2008): "Gravity : An Emergent Perspective"
Steve Carlip (2007): "Symmetries, Horizons, and Black Hole Entropy"

Despite many attempts in the last 80 years, a final quantum theory of gravity is elusive. There are various approaches, which all have their merits and shortcomings [1,2]. A major problem in the search for a final theory is the lack of empirical tests so far. This problem is usually attributed to the fact that the Planck scale, on which quantum gravity effects are supposed to become strong, is far remote from any other relevant scale. Expressed in energy units, the Planck scale is 15 orders of magnitude higher than even the energy reachable at the Large Hadron Collider (LHC) in Geneva. It is thus hopeless to probe the Planck scale directly by scattering experiments.

In our prize-winning essay [3], we have addressed the question whether effects of quantum gravity can be observed in a cosmological context. More precisely, we have investigated the presence of possible effects in the anisotropy spectrum of the cosmic microwave background (CMB) radiation.

But given the presence of many approaches, which framework should one use for the calculations? We have decided to be as conservative as possible and to base our investigation on quantum geometrodynamics, the direct quantization of Einstein's theory. The central equation in this approach is the Wheeler-DeWitt equation, named after the pioneering work of Bryce DeWitt and John Wheeler [4]. It is a conservative approach because the Wheeler-DeWitt equation is the quantum equation that directly leads to general relativity in the semiclassical limit. It possesses for gravity the same value that the Schrödinger equation has for mechanics.

While the Wheeler-DeWitt equation is difficult to solve in full generality, it can be treated in an approximation scheme that is similar to a scheme known from molecular physics - the Born-Oppenheimer approximation. It basically consists of an expansion with respect to the Planck energy. It is thus assumed that the relevant expansion parameter is (the square of) the relevant energy scale over the Planck energy. A Born-Oppenheimer scheme of this type has been applied to gravity in [5]. In this way, one first arrives at the limit of quantum field theory on a fixed background. The next order then gives quantum-gravitational corrections that are inversely proportional to the Planck mass squared. It is these correction terms that we have evaluated for the CMB. The quantitative discussion, on which our essay is based, is presented in [6]. We assume that the Universe underwent a period of inflationary expansion at an early stage and that it was this inflation that produced the CMB anisotropies out of which all structure in the Universe evolved.

What are the results? The calculations show that the quantum-gravitational correction terms lead to a modification of the anisotropy power spectrum that is most pronounced for large scales, that is, large angular separations at the sky. More precisely, one finds a suppression of power at large scales. Such a suppression can, in principle, be observed. Since up to now no such signal has been identified, not even in the measurements of the WMAP satellite, we can find from our investigation only an upper limit on the expansion rate of the inflationary Universe. The effect is therefore too small to be seen, it seems, although it is expected to be considerably larger than quantum-gravitational effects in the laboratory.

A similar investigation was done for loop quantum cosmology [7]. It was found there that quantum gravitational effects lead to an enhancement of the power at large scales, instead of a suppression. These considerations may thus be able to discriminate between different approaches to quantum gravity.

What are the implications for future research? It remains to be seen whether the size of quantum-gravitational corrections terms can become large enough to be observable in other circumstances. One may think of the polarization of the CMB anisotropies or at the correlations functions of galaxies. Such investigations are important because there will be no fundamental progress in quantum gravity research without observational guidance. We hope that our essay will stimulate research in this direction.

References
[1] C. Kiefer, "Quantum Gravity" (Oxford University Press, Oxford, 3rd edition, 2012).
[2] S. Carlip, "Quantum gravity: a progress report", Reports on Progress in Physics, 64, 885-942 (2001).Abstract.
[3] C. Kiefer and M. Krämer, "Can effects of quantum gravity be observed in the cosmic microwave background?",  To appear in Int. J. Mod. Phys. D. Available at: arXiv:1205.5161 [gr-qc],
[4] B. S. DeWitt, "Quantum theory of gravity. I. The canonical theory", Phys. Rev., 160, 1113-1148 (1967). Abstract; J. A. Wheeler, "Superspace and the nature of quantum geometrodynamics", in: "Battelle rencontres", ed. by C. M. DeWitt and J. A. Wheeler (Benjamin, New York, 1968), pp. 242-307.
[5] C. Kiefer and T. P. Singh, "Quantum gravitational correction terms to the functional Schrödinger equation", Phys. Rev. D, 44, 1067-1076 (1991).Abstract.
[6] C. Kiefer and M. Krämer, "Quantum Gravitational Contributions to the CMB Anisotropy Spectrum", Phys. Rev. Lett., 108, 021301 (2012).Abstract.
[7] M. Bojowald, G. Calcagni, and S. Tsujikawa, "Observational Constraints on Loop Quantum Cosmology", Phys. Rev. Lett., 107, 211302 (2012). Abstract.